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1. Ex-vivo quantification of ovine pia arachnoid complex biomechanical properties under uniaxial tension

   https://doi.org/10.1186/s12987-020-00229-w  

   Conley Natividad, Gabryel ; Theodossiou, Sophia K. ; Schiele, Nathan R. ; Murdoch, Gordon K. ; Tsamis, Alkiviadis ; Tanner, Bertrand ; Potirniche, Gabriel ; Mortazavi, Martin ; Vorp, David A. ; Martin, Bryn A. ( December 2020 , Fluids and Barriers of the CNS)

   null (Ed.)

   Abstract Background The pia arachnoid complex (PAC) is a cerebrospinal fluid-filled tissue conglomerate that surrounds the brain and spinal cord. Pia mater adheres directly to the surface of the brain while the arachnoid mater adheres to the deep surface of the dura mater. Collagen fibers, known as subarachnoid trabeculae (SAT) fibers, and microvascular structure lie intermediately to the pia and arachnoid meninges. Due to its structural role, alterations to the biomechanical properties of the PAC may change surface stress loading in traumatic brain injury (TBI) caused by sub-concussive hits. The aim of this study was to quantify the mechanical and morphological properties of ovine PAC. Methods Ovine brain samples (n = 10) were removed from the skull and tissue was harvested within 30 min post-mortem. To access the PAC, ovine skulls were split medially from the occipital region down the nasal bone on the superior and inferior aspects of the skull. A template was used to remove arachnoid samples from the left and right sides of the frontal and occipital regions of the brain. 10 ex-vivo samples were tested with uniaxial tension at 2 mm s −1 , average strain rate of 0.59 s −1 , until failure at < 5 h post extraction. The force and displacement data were acquired at 100 Hz. PAC tissue collagen fiber microstructure was characterized using second-harmonic generation (SHG) imaging on a subset of n = 4 stained tissue samples. To differentiate transverse blood vessels from SAT by visualization of cell nuclei and endothelial cells, samples were stained with DAPI and anti-von Willebrand Factor, respectively. The Mooney-Rivlin model for average stress–strain curve fit was used to model PAC material properties. Results The elastic modulus, ultimate stress, and ultimate strain were found to be 7.7 ± 3.0, 2.7 ± 0.76 MPa, and 0.60 ± 0.13, respectively. No statistical significance was found across brain dissection locations in terms of biomechanical properties. SHG images were post-processed to obtain average SAT fiber intersection density, concentration, porosity, tortuosity, segment length, orientation, radial counts, and diameter as 0.23, 26.14, 73.86%, 1.07 ± 0.28, 17.33 ± 15.25 µm, 84.66 ± 49.18°, 8.15%, 3.46 ± 1.62 µm, respectively. Conclusion For the sizes, strain, and strain rates tested, our results suggest that ovine PAC mechanical behavior is isotropic, and that the Mooney-Rivlin model is an appropriate curve-fitting constitutive equation for obtaining material parameters of PAC tissues. 

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2. Application of Digital Image Correlation (DIC) to the Measurement of Strain Concentration of a PVA Dual-Crosslink Hydrogel Under Large Deformation

   https://doi.org/10.1007/s11340-019-00520-4  

   Liu, M. ; Guo, J. ; Hui, C.-Y. ; Zehnder, A. T. ( January 2019 , Experimental Mechanics)

   Hydrogels are a class of soft, highly deformable materials formed by swelling a network of polymer chains in water. With mechanical properties that mimic biological materials, hydrogels are often proposed for load bearing biomedical or other applications in which their deformation and failure properties will be important. To study the failure of such materials a means for the measurement of deformation fields beyond simple uniaxial tension tests is required. As a non-contact, full-field deformation measurement method, Digital Image Correlation (DIC) is a good candidate for such studies. The application of DIC to hydrogels is studied here with the goal of establishing the accuracy of DIC when applied to hydrogels in the presence of large strains and large strain gradients. Experimental details such as how to form a durable speckle pattern on a material that is 90% water are discussed. DIC is used to measure the strain field in tension loaded samples containing a central hole, a circular edge notch and a sharp crack. Using a nonlinear, large deformation constitutive model, these experiments are modeled using the finite element method (FEM). Excellent agreement between FEM and DIC results for all three geometries shows that the DIC measurements are accurate up to strains of over 10, even in the presence of very high strain gradients near a crack tip. The method is then applied to verify a theoretical prediction that the deformation field in a cracked sample under relaxation loading, i.e. constant applied boundary displacement, is stationary in time even as the stress relaxes by a factor of three. 

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3. Origins of strain localization in a silver-based flexible ink under tensile load

   https://doi.org/10.1088/2058-8585/ac414c  

   Li, Qiushi ; Pierron, Olivier ; Antoniou, Antonia ( December 2021 , Flexible and Printed Electronics)

   Abstract Flexible electronics often employ composite inks consisting of conductive flakes embedded in a polymer matrix to transmit electrical signal. Recently, localized necking was identified as a cause of a substantial increase in normalized resistance with applied strain thereby adversely impacting electrical performance. The current study explores two possible contributing factors for the formation of such localization—ink surface roughness and local variations in silver flake volume fraction. Uniaxial tension experiments of a DuPont 5025 type ink are used to inform a constitutive model implemented using finite element method on different substrates. Surface roughness was modeled by sinusoidal variation in ink height, whose amplitude and wavelength are informed by experimental laser profilometry scan data. Local flake fraction variations obtained from experimental measurements before applying any strain, were modeled as local variations in the elastic modulus according to an inverse rule of mixtures between the silver flake and acrylic binder material properties. The study identified that the ink height roughness is the most impactful contributor to the subsequent strain localization. The substrate elastic properties impact the number and magnitude of localization bands, with the stiffer substrate delocalizing strain and averting catastrophic crack formation seen with a more compliant substrate. The model incorporating surface roughness closely matches experimental measurements of local strain across different substrates. The study can inform designers of the adverse impact of ink surface roughness on localization and subsequent detrimental increase of the resistance. 

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4. Analysis of the compressible, isotropic, neo-Hookean hyperelastic model

   https://doi.org/10.1007/s11012-022-01633-2  

   Kossa, Attila ; Valentine, Megan T. ; McMeeking, Robert M. ( January 2023 , Meccanica)

   The most widely-used representation of the compressible, isotropic, neo-Hookean hyperelastic model is considered in this paper. The version under investigation is that which is implemented in the commercial finite element software ABAQUS, ANSYS and COMSOL. Transverse stretch solutions are obtained for the following homogeneous deformations: uniaxial loading, equibiaxial loading in plane stress, and uniaxial loading in plane strain. The ground-state Poisson’s ratio is used to parameterize the constitutive model, and stress solutions are computed numerically for the physically permitted range of its values. Despite its broad application to a number of engineering problems, the physical limitations of the model, particularly in the small to moderate stretch regimes, are not explored. In this work, we describe and analyze results and make some critical observations, underlining the model’s advantages and limitations. For example, a snap-back feature of the transverse stretch is identified in uniaxial compression, a physically undesirable behavior unless validated by experimental data. The domain of this non-unique solution is determined in terms of the ground-state Poisson’s ratio and the state of stretch and stress. The analyses we perform are essential to enable the understanding of the characteristics of the standard, compressible, isotropic, neo-Hookean model used in ABAQUS, ANSYS and COMSOL. In addition, our results provide a framework for the parameter-fitting procedure needed to characterize this standard, compressible, isotropic neo-Hookean model in terms of experimental data.

    

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5. On the Transversely Isotropic, Hyperelastic Response of Central Nervous System White Matter Using a Hybrid Approach

   https://doi.org/10.1115/1.4049168  

   Pan, Yi ; Shreiber, David I. ; Pelegri, Assimina A. ( February 2021 , Journal of Engineering and Science in Medical Diagnostics and Therapy)

   Abstract A numerical and experimental hybrid approach is developed to study the constitutive behavior of the central nervous system white matter. A published transversely isotropic hyperelastic strain energy function is reviewed and used to determine stress–strain relationships for three idealized, simple loading scenarios. The proposed constitutive model is simplified to a three-parameter hyperelastic model by assuming the white matter's incompressibility. Due to a lack of experimental data in all three loading scenarios, a finite element model that accounts for microstructural axons and their kinematics is developed to simulate behaviors in simple shear loading scenarios to supplement existing uniaxial tensile test data. The parameters of the transversely isotropic hyperelastic material model are determined regressively using the hybrid data. The results highlight that a hybrid numerical virtual test coupled with experimental data, can determine the transversely isotropic hyperelastic model. It is noted that the model is not limited to small strains and can be applied to large deformations. 

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